Complete 64-state quantum comparison and retained field evolution

Abstract

Two contacts can agree as a comparison while changing the systems that carry them. For an explicit pair of eight-state systems, we derive a comparison identity on all 64 states: its squared difference depends only on the relative field phase. We construct a unitary event that retains both comparison outcomes and every earlier record. Exchange symmetry fixes a signed load within a stated affine class, and reciprocal weights give normal stationary sources on discrete field levels. On a continuous load, the same event has no normal stationary source when the waiting evolution preserves that load. A specified oscillator rotation changes the conclusion: a two-event energy bound yields a normal stationary source with finite energy. The complete event also imposes an exact work constraint. These results constrain the field evolution and work carrier needed to connect retained comparison to a physical interaction law.